Slopes of Lines Geometry

SLOPE

Slope Slope is usually represented by the variable m Always start with the point farthest right

Examples Find the slope that passes through the following points. (0,6) and (5,2) (-3,0) and (4,7)

Examples Find the slope that passes through the following points. (-4,-3) and (3,-3) (2,1) and (2,-4)

Slope Slope can be interpreted as a rate of change, describing how a quantity y changes in relation to quantity x. The slope of a line can also be used to identify the coordinates of any point on the line.

Example A pilot flies a plane from Columbus, Ohio, to Orlando, Florida. After 0.5 hours, the plane reaches its cruising altitude and is 620 miles from Orlando. Half an hour later, the plane is 450 miles from Orlando. How far was the plane from Orlando 1.25 hours after takeoff?

Example In 2006, 500 million songs were legally downloaded from the Internet. In 2004, 200 million songs were legally downloaded. Use the data given to graph the line that models the number of songs legally downloaded, y, as a function of time, x, in years. Find the slope of the line, and interpret its meaning. If this trend continues at the same rate, how many songs will be legally downloaded in 2020?

SLOPES OF PARALLEL LINES In a coordinate plane, two nonvertical lines are parallel if and only if they have the same slope. Any two vertical lines are parallel

Example Line p passes through (0, -3) and (1, -2). Line m passes through (5,4) and (-4, -4). Line n passes through (-6, -1) and (3, 7). Find the slope of each line. Which lines are parallel?

SLOPES OF PERPENDICULAR LINES In a coordinate plane, two nonvertical lines are perpendicular if and only if the product of their slopes is -1. Vertical and horizontal lines are perpendicular.

Example Determine whether AB and CD are parallel, perpendicular, or neither. A(14, 13), B(-11, 0), C(-3, 7), D(-4, -5) A(3, 6), B(-9, 2), C(5, 4), D(2, 3)